LMFDB - Embedded newform 1050.3.p.c.451.1

Newspace parameters

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.p (of order $6$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.151613669376.6
Defining polynomial:	$ x^{8} - 12x^{6} + 95x^{4} - 588x^{2} + 2401 $ x^8 - 12x^6 + 95x^4 - 588*x^2 + 2401
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			451.1
Root			$2.56149 - 0.662382i$ of defining polynomial
Character	$\chi$	$=$	1050.451
Dual form			1050.3.p.c.901.1

$q$-expansion

$f(q)$	$=$	$q+(-0.707107 - 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +2.44949i q^{6} +(-0.440173 - 6.98615i) q^{7} +2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +2.44949i q^{6} +(-0.440173 - 6.98615i) q^{7} +2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(-3.76860 + 6.52741i) q^{11} +(3.00000 - 1.73205i) q^{12} -21.3906i q^{13} +(-8.24500 + 5.47905i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(18.1757 + 10.4937i) q^{17} +(2.12132 - 3.67423i) q^{18} +(20.8728 - 12.0509i) q^{19} +(-5.38992 + 10.8604i) q^{21} +10.6592 q^{22} +(2.79005 + 4.83250i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(-26.1981 + 15.1255i) q^{26} -5.19615i q^{27} +(12.5405 + 6.22374i) q^{28} -9.96625 q^{29} +(5.70073 + 3.29132i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(11.3058 - 6.52741i) q^{33} -29.6807i q^{34} -6.00000 q^{36} +(11.1983 + 19.3960i) q^{37} +(-29.5187 - 17.0426i) q^{38} +(-18.5248 + 32.0860i) q^{39} -51.0827i q^{41} +(17.1125 - 1.07820i) q^{42} -34.7656 q^{43} +(-7.53720 - 13.0548i) q^{44} +(3.94572 - 6.83419i) q^{46} +(67.2462 - 38.8246i) q^{47} +6.92820i q^{48} +(-48.6125 + 6.15023i) q^{49} +(-18.1757 - 31.4812i) q^{51} +(37.0497 + 21.3906i) q^{52} +(24.8989 - 43.1262i) q^{53} +(-6.36396 + 3.67423i) q^{54} +(-1.24500 - 19.7598i) q^{56} -41.7457 q^{57} +(7.04720 + 12.2061i) q^{58} +(72.9362 + 42.1098i) q^{59} +(-72.4404 + 41.8235i) q^{61} -9.30925i q^{62} +(17.4903 - 11.6228i) q^{63} +8.00000 q^{64} +(-15.9888 - 9.23115i) q^{66} +(33.2911 - 57.6618i) q^{67} +(-36.3513 + 20.9874i) q^{68} -9.66501i q^{69} -68.1049 q^{71} +(4.24264 + 7.34847i) q^{72} +(-75.9128 - 43.8283i) q^{73} +(15.8368 - 27.4301i) q^{74} +48.2038i q^{76} +(47.2603 + 23.4548i) q^{77} +52.3962 q^{78} +(-49.3730 - 85.5165i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-62.5632 + 36.1209i) q^{82} -26.9448i q^{83} +(-13.4209 - 20.1960i) q^{84} +(24.5830 + 42.5790i) q^{86} +(14.9494 + 8.63103i) q^{87} +(-10.6592 + 18.4623i) q^{88} +(12.0453 - 6.95436i) q^{89} +(-149.438 + 9.41559i) q^{91} -11.1602 q^{92} +(-5.70073 - 9.87395i) q^{93} +(-95.1005 - 54.9063i) q^{94} +(8.48528 - 4.89898i) q^{96} -3.69132i q^{97} +(41.9067 + 55.1890i) q^{98} -22.6116 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{3} - 8 q^{4} + 12 q^{9}+O(q^{10}) $ 8 * q - 12 * q^3 - 8 * q^4 + 12 * q^9	$ 8 q - 12 q^{3} - 8 q^{4} + 12 q^{9} - 4 q^{11} + 24 q^{12} - 16 q^{14} - 16 q^{16} - 24 q^{17} + 72 q^{19} + 24 q^{22} + 60 q^{23} - 72 q^{26} - 24 q^{29} + 96 q^{31} + 12 q^{33} - 48 q^{36} - 24 q^{37} - 180 q^{38} - 12 q^{39} + 12 q^{42} - 112 q^{43} - 8 q^{44} + 32 q^{46} + 84 q^{47} - 264 q^{49} + 24 q^{51} + 24 q^{52} + 44 q^{53} + 40 q^{56} - 144 q^{57} + 104 q^{58} + 312 q^{59} - 204 q^{61} + 64 q^{64} - 36 q^{66} + 120 q^{67} + 48 q^{68} - 64 q^{71} + 84 q^{73} - 16 q^{74} + 228 q^{77} + 144 q^{78} - 144 q^{79} - 36 q^{81} - 60 q^{82} + 176 q^{86} + 36 q^{87} - 24 q^{88} - 336 q^{89} - 296 q^{91} - 240 q^{92} - 96 q^{93} + 36 q^{94} - 24 q^{99}+O(q^{100}) $ 8 * q - 12 * q^3 - 8 * q^4 + 12 * q^9 - 4 * q^11 + 24 * q^12 - 16 * q^14 - 16 * q^16 - 24 * q^17 + 72 * q^19 + 24 * q^22 + 60 * q^23 - 72 * q^26 - 24 * q^29 + 96 * q^31 + 12 * q^33 - 48 * q^36 - 24 * q^37 - 180 * q^38 - 12 * q^39 + 12 * q^42 - 112 * q^43 - 8 * q^44 + 32 * q^46 + 84 * q^47 - 264 * q^49 + 24 * q^51 + 24 * q^52 + 44 * q^53 + 40 * q^56 - 144 * q^57 + 104 * q^58 + 312 * q^59 - 204 * q^61 + 64 * q^64 - 36 * q^66 + 120 * q^67 + 48 * q^68 - 64 * q^71 + 84 * q^73 - 16 * q^74 + 228 * q^77 + 144 * q^78 - 144 * q^79 - 36 * q^81 - 60 * q^82 + 176 * q^86 + 36 * q^87 - 24 * q^88 - 336 * q^89 - 296 * q^91 - 240 * q^92 - 96 * q^93 + 36 * q^94 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.707107	−	1.22474i	−0.353553	−	0.612372i
$2$	−0.707107	−	1.22474i	−0.353553	−	0.612372i
$3$	−1.50000	−	0.866025i	−0.500000	−	0.288675i
$3$	−1.50000	−	0.866025i	−0.500000	−	0.288675i
$4$	−1.00000	+	1.73205i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$			2.44949i			0.408248i
$7$	−0.440173	−	6.98615i	−0.0628819	−	0.998021i
$7$	−0.440173	−	6.98615i	−0.0628819	−	0.998021i
$8$	2.82843			0.353553
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$		0			0
$11$	−3.76860	+	6.52741i	−0.342600	+	0.593401i	−0.984915	−	0.173040i	$-0.944641\pi$
$11$	−3.76860	+	6.52741i	−0.342600	+	0.593401i	0.642315	+	0.766441i	$0.277974\pi$
$12$	3.00000	−	1.73205i	0.250000	−	0.144338i
$13$		−	21.3906i		−	1.64543i	−0.568451	−	0.822717i	$-0.692457\pi$
$13$		−	21.3906i		−	1.64543i	0.568451	−	0.822717i	$-0.307543\pi$
$14$	−8.24500	+	5.47905i	−0.588928	+	0.391361i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	18.1757	+	10.4937i	1.06916	+	0.617278i	0.927951	−	0.372703i	$-0.121569\pi$
$17$	18.1757	+	10.4937i	1.06916	+	0.617278i	0.141205	+	0.989980i	$0.454902\pi$
$18$	2.12132	−	3.67423i	0.117851	−	0.204124i
$19$	20.8728	−	12.0509i	1.09857	−	0.634260i	0.162726	−	0.986671i	$-0.447971\pi$
$19$	20.8728	−	12.0509i	1.09857	−	0.634260i	0.935845	+	0.352411i	$0.114638\pi$
$20$		0			0
$21$	−5.38992	+	10.8604i	−0.256663	+	0.517163i
$22$	10.6592			0.484510
$23$	2.79005	+	4.83250i	0.121306	+	0.210109i	0.920283	−	0.391253i	$-0.127958\pi$
$23$	2.79005	+	4.83250i	0.121306	+	0.210109i	−0.798977	+	0.601362i	$0.794625\pi$
$24$	−4.24264	−	2.44949i	−0.176777	−	0.102062i
$25$		0			0
$26$	−26.1981	+	15.1255i	−1.00762	+	0.581749i
$27$		−	5.19615i		−	0.192450i
$28$	12.5405	+	6.22374i	0.447876	+	0.222277i
$29$	−9.96625			−0.343664			−0.171832	−	0.985126i	$-0.554969\pi$
$29$	−9.96625			−0.343664			−0.171832	+	0.985126i	$0.554969\pi$
$30$		0			0
$31$	5.70073	+	3.29132i	0.183894	+	0.106171i	0.589121	−	0.808045i	$-0.299474\pi$
$31$	5.70073	+	3.29132i	0.183894	+	0.106171i	−0.405227	+	0.914216i	$0.632807\pi$
$32$	−2.82843	+	4.89898i	−0.0883883	+	0.153093i
$33$	11.3058	−	6.52741i	0.342600	−	0.197800i
$34$		−	29.6807i		−	0.872962i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	11.1983	+	19.3960i	0.302656	+	0.524216i	0.976737	−	0.214442i	$-0.0687933\pi$
$37$	11.1983	+	19.3960i	0.302656	+	0.524216i	−0.674080	+	0.738658i	$0.735460\pi$
$38$	−29.5187	−	17.0426i	−0.776807	−	0.448490i
$39$	−18.5248	+	32.0860i	−0.474996	+	0.822717i
$40$		0			0
$41$		−	51.0827i		−	1.24592i	−0.782254	−	0.622959i	$-0.785930\pi$
$41$		−	51.0827i		−	1.24592i	0.782254	−	0.622959i	$-0.214070\pi$
$42$	17.1125	−	1.07820i	0.407440	−	0.0256714i
$43$	−34.7656			−0.808503			−0.404252	−	0.914648i	$-0.632468\pi$
$43$	−34.7656			−0.808503			−0.404252	+	0.914648i	$0.632468\pi$
$44$	−7.53720	−	13.0548i	−0.171300	−	0.296700i
$45$		0			0
$46$	3.94572	−	6.83419i	0.0857766	−	0.148569i
$47$	67.2462	−	38.8246i	1.43077	−	0.826056i	0.433591	−	0.901110i	$-0.357246\pi$
$47$	67.2462	−	38.8246i	1.43077	−	0.826056i	0.997179	+	0.0750536i	$0.0239128\pi$
$48$			6.92820i			0.144338i
$49$	−48.6125	+	6.15023i	−0.992092	+	0.125515i
$50$		0			0
$51$	−18.1757	−	31.4812i	−0.356385	−	0.617278i
$52$	37.0497	+	21.3906i	0.712494	+	0.411359i
$53$	24.8989	−	43.1262i	0.469791	−	0.813703i	−0.529612	−	0.848240i	$-0.677662\pi$
$53$	24.8989	−	43.1262i	0.469791	−	0.813703i	0.999403	+	0.0345374i	$0.0109958\pi$
$54$	−6.36396	+	3.67423i	−0.117851	+	0.0680414i
$55$		0			0
$56$	−1.24500	−	19.7598i	−0.0222321	−	0.352854i
$57$	−41.7457			−0.732381
$58$	7.04720	+	12.2061i	0.121504	+	0.210450i
$59$	72.9362	+	42.1098i	1.23621	+	0.713725i	0.968317	−	0.249725i	$-0.0803401\pi$
$59$	72.9362	+	42.1098i	1.23621	+	0.713725i	0.267890	+	0.963449i	$0.413673\pi$
$60$		0			0
$61$	−72.4404	+	41.8235i	−1.18755	+	0.685631i	−0.957749	−	0.287607i	$-0.907140\pi$
$61$	−72.4404	+	41.8235i	−1.18755	+	0.685631i	−0.229799	+	0.973238i	$0.573807\pi$
$62$		−	9.30925i		−	0.150149i
$63$	17.4903	−	11.6228i	0.277624	−	0.184489i
$64$	8.00000			0.125000
$65$		0			0
$66$	−15.9888	−	9.23115i	−0.242255	−	0.139866i
$67$	33.2911	−	57.6618i	0.496882	−	0.860625i	−0.503112	−	0.864221i	$-0.667812\pi$
$67$	33.2911	−	57.6618i	0.496882	−	0.860625i	0.999994	+	0.00359682i	$0.00114491\pi$
$68$	−36.3513	+	20.9874i	−0.534578	+	0.308639i
$69$		−	9.66501i		−	0.140073i
$70$		0			0
$71$	−68.1049			−0.959224			−0.479612	−	0.877481i	$-0.659223\pi$
$71$	−68.1049			−0.959224			−0.479612	+	0.877481i	$0.659223\pi$
$72$	4.24264	+	7.34847i	0.0589256	+	0.102062i
$73$	−75.9128	−	43.8283i	−1.03990	−	0.600387i	−0.120096	−	0.992762i	$-0.538320\pi$
$73$	−75.9128	−	43.8283i	−1.03990	−	0.600387i	−0.919805	+	0.392375i	$0.871654\pi$
$74$	15.8368	−	27.4301i	0.214010	−	0.370677i
$75$		0			0
$76$			48.2038i			0.634260i
$77$	47.2603	+	23.4548i	0.613770	+	0.304608i
$78$	52.3962			0.671746
$79$	−49.3730	−	85.5165i	−0.624974	−	1.08249i	−0.988546	−	0.150921i	$-0.951776\pi$
$79$	−49.3730	−	85.5165i	−0.624974	−	1.08249i	0.363572	−	0.931566i	$-0.381557\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	−62.5632	+	36.1209i	−0.762966	+	0.440499i
$83$		−	26.9448i		−	0.324636i	−0.986739	−	0.162318i	$-0.948103\pi$
$83$		−	26.9448i		−	0.324636i	0.986739	−	0.162318i	$-0.0518970\pi$
$84$	−13.4209	−	20.1960i	−0.159772	−	0.240429i
$85$		0			0
$86$	24.5830	+	42.5790i	0.285849	+	0.495105i
$87$	14.9494	+	8.63103i	0.171832	+	0.0992072i
$88$	−10.6592	+	18.4623i	−0.121127	+	0.209799i
$89$	12.0453	−	6.95436i	0.135341	−	0.0781389i	−0.430801	−	0.902447i	$-0.641769\pi$
$89$	12.0453	−	6.95436i	0.135341	−	0.0781389i	0.566142	+	0.824308i	$0.308436\pi$
$90$		0			0
$91$	−149.438	+	9.41559i	−1.64218	+	0.103468i
$92$	−11.1602			−0.121306
$93$	−5.70073	−	9.87395i	−0.0612981	−	0.106171i
$94$	−95.1005	−	54.9063i	−1.01171	−	0.584110i
$95$		0			0
$96$	8.48528	−	4.89898i	0.0883883	−	0.0510310i
$97$		−	3.69132i		−	0.0380549i	−0.999819	−	0.0190274i	$-0.993943\pi$
$97$		−	3.69132i		−	0.0380549i	0.999819	−	0.0190274i	$-0.00605698\pi$
$98$	41.9067	+	55.1890i	0.427619	+	0.563153i
$99$	−22.6116			−0.228400
$100$		0			0
$101$	−158.170	−	91.3195i	−1.56604	−	0.904154i	−0.996624	−	0.0821041i	$-0.973836\pi$
$101$	−158.170	−	91.3195i	−1.56604	−	0.904154i	−0.569416	−	0.822049i	$-0.692831\pi$
$102$	−25.7043	+	44.5211i	−0.252003	+	0.436481i
$103$	−78.8521	+	45.5253i	−0.765555	+	0.441993i	−0.831287	−	0.555844i	$-0.812395\pi$
$103$	−78.8521	+	45.5253i	−0.765555	+	0.441993i	0.0657318	+	0.997837i	$0.479062\pi$
$104$		−	60.5019i		−	0.581749i
$105$		0			0
$106$	−70.4249			−0.664385
$107$	−25.7682	−	44.6318i	−0.240824	−	0.417120i	0.720125	−	0.693844i	$-0.244084\pi$
$107$	−25.7682	−	44.6318i	−0.240824	−	0.417120i	−0.960949	+	0.276724i	$0.910751\pi$
$108$	9.00000	+	5.19615i	0.0833333	+	0.0481125i
$109$	−19.1807	+	33.2219i	−0.175970	+	0.304788i	−0.940496	−	0.339804i	$-0.889639\pi$
$109$	−19.1807	+	33.2219i	−0.175970	+	0.304788i	0.764527	+	0.644592i	$0.222973\pi$
$110$		0			0
$111$		−	38.7920i		−	0.349477i
$112$	−23.3204	+	15.4971i	−0.208218	+	0.138367i
$113$	−198.558			−1.75715			−0.878573	−	0.477608i	$-0.841504\pi$
$113$	−198.558			−1.75715			−0.878573	+	0.477608i	$0.841504\pi$
$114$	29.5187	+	51.1278i	0.258936	+	0.448490i
$115$		0			0
$116$	9.96625	−	17.2621i	0.0859160	−	0.148811i
$117$	55.5745	−	32.0860i	0.474996	−	0.274239i
$118$		−	119.104i		−	1.00936i
$119$	65.3102	−	131.597i	0.548825	−	1.10586i
$120$		0			0
$121$	32.0953	+	55.5907i	0.265250	+	0.459427i
$122$	102.446	+	59.1474i	0.839723	+	0.484814i
$123$	−44.2389	+	76.6240i	−0.359666	+	0.622959i
$124$	−11.4015	+	6.58263i	−0.0919472	+	0.0530857i
$125$		0			0
$126$	−26.6025	−	13.2026i	−0.211131	−	0.104782i
$127$	−74.1132			−0.583569			−0.291784	−	0.956484i	$-0.594249\pi$
$127$	−74.1132			−0.583569			−0.291784	+	0.956484i	$0.594249\pi$
$128$	−5.65685	−	9.79796i	−0.0441942	−	0.0765466i
$129$	52.1485	+	30.1079i	0.404252	+	0.233395i
$130$		0			0
$131$	17.3500	−	10.0170i	0.132443	−	0.0764657i	−0.432315	−	0.901723i	$-0.642303\pi$
$131$	17.3500	−	10.0170i	0.132443	−	0.0764657i	0.564757	+	0.825257i	$0.308970\pi$
$132$			26.1096i			0.197800i
$133$	−93.3773	−	140.516i	−0.702085	−	1.05651i
$134$	−94.1614			−0.702697
$135$		0			0
$136$	51.4085	+	29.6807i	0.378004	+	0.218241i
$137$	43.0853	−	74.6259i	0.314491	−	0.544715i	−0.664838	−	0.746988i	$-0.731499\pi$
$137$	43.0853	−	74.6259i	0.314491	−	0.544715i	0.979329	+	0.202273i	$0.0648328\pi$
$138$	−11.8372	+	6.83419i	−0.0857766	+	0.0495231i
$139$			232.502i			1.67268i	0.548213	+	0.836339i	$0.315308\pi$
$139$			232.502i			1.67268i	−0.548213	+	0.836339i	$0.684692\pi$
$140$		0			0
$141$	−134.492			−0.953847
$142$	48.1574	+	83.4111i	0.339137	+	0.587402i
$143$	139.625	+	80.6128i	0.976402	+	0.563726i
$144$	6.00000	−	10.3923i	0.0416667	−	0.0721688i
$145$		0			0
$146$			123.965i			0.849076i
$147$	78.2450	+	32.8743i	0.532279	+	0.223635i
$148$	−44.7931			−0.302656
$149$	109.963	+	190.462i	0.738008	+	1.27827i	0.953391	+	0.301738i	$0.0975666\pi$
$149$	109.963	+	190.462i	0.738008	+	1.27827i	−0.215383	+	0.976530i	$0.569100\pi$
$150$		0			0
$151$	130.461	−	225.965i	0.863980	−	1.49646i	−0.00407633	−	0.999992i	$-0.501298\pi$
$151$	130.461	−	225.965i	0.863980	−	1.49646i	0.868056	−	0.496466i	$-0.165369\pi$
$152$	59.0373	−	34.0852i	0.388403	−	0.224245i
$153$			62.9623i			0.411518i
$154$	−4.69190	−	74.4668i	−0.0304669	−	0.483551i
$155$		0			0
$156$	−37.0497	−	64.1719i	−0.237498	−	0.411359i
$157$	−98.8921	−	57.0954i	−0.629886	−	0.363665i	0.150822	−	0.988561i	$-0.451808\pi$
$157$	−98.8921	−	57.0954i	−0.629886	−	0.363665i	−0.780708	+	0.624896i	$0.785141\pi$
$158$	−69.8239	+	120.939i	−0.441923	+	0.765434i
$159$	−74.6968	+	43.1262i	−0.469791	+	0.271234i
$160$		0			0
$161$	32.5325	−	21.6188i	0.202065	−	0.134278i
$162$	12.7279			0.0785674
$163$	−24.3581	−	42.1894i	−0.149436	−	0.258831i	0.781583	−	0.623801i	$-0.214412\pi$
$163$	−24.3581	−	42.1894i	−0.149436	−	0.258831i	−0.931019	+	0.364970i	$0.881079\pi$
$164$	88.4777	+	51.0827i	0.539498	+	0.311480i
$165$		0			0
$166$	−33.0005	+	19.0528i	−0.198798	+	0.114776i
$167$			49.6127i			0.297082i	0.988906	+	0.148541i	$0.0474577\pi$
$167$			49.6127i			0.297082i	−0.988906	+	0.148541i	$0.952542\pi$
$168$	−15.2450	+	30.7179i	−0.0907440	+	0.182845i
$169$	−288.560			−1.70745
$170$		0			0
$171$	62.6185	+	36.1528i	0.366190	+	0.211420i
$172$	34.7656	−	60.2159i	0.202126	−	0.350092i
$173$	−203.811	+	117.670i	−1.17810	+	0.680176i	−0.955574	−	0.294751i	$-0.904763\pi$
$173$	−203.811	+	117.670i	−1.17810	+	0.680176i	−0.222525	+	0.974927i	$0.571430\pi$
$174$		−	24.4122i		−	0.140300i
$175$		0			0
$176$	30.1488			0.171300
$177$	−72.9362	−	126.329i	−0.412069	−	0.713725i
$178$	−17.0346	−	9.83495i	−0.0957002	−	0.0552525i
$179$	22.1049	−	38.2868i	0.123491	−	0.213893i	−0.797651	−	0.603119i	$-0.793924\pi$
$179$	22.1049	−	38.2868i	0.123491	−	0.213893i	0.921142	+	0.389226i	$0.127258\pi$
$180$		0			0
$181$			117.049i			0.646679i	0.946283	+	0.323340i	$0.104806\pi$
$181$			117.049i			0.646679i	−0.946283	+	0.323340i	$0.895194\pi$
$182$	117.200	+	176.366i	0.643958	+	0.969043i
$183$	144.881			0.791699
$184$	7.89145	+	13.6684i	0.0428883	+	0.0742847i
$185$		0			0
$186$	−8.06204	+	13.9639i	−0.0433443	+	0.0750746i
$187$	−136.994	+	79.0933i	−0.732586	+	0.422959i
$188$			155.299i			0.826056i
$189$	−36.3011	+	2.28721i	−0.192069	+	0.0121016i
$190$		0			0
$191$	−117.156	−	202.920i	−0.613383	−	1.06241i	−0.990666	−	0.136313i	$-0.956475\pi$
$191$	−117.156	−	202.920i	−0.613383	−	1.06241i	0.377283	−	0.926098i	$-0.376858\pi$
$192$	−12.0000	−	6.92820i	−0.0625000	−	0.0360844i
$193$	9.78252	−	16.9438i	0.0506866	−	0.0877918i	−0.839569	−	0.543253i	$-0.817192\pi$
$193$	9.78252	−	16.9438i	0.0506866	−	0.0877918i	0.890256	+	0.455461i	$0.150526\pi$
$194$	−4.52093	+	2.61016i	−0.0233037	+	0.0134544i
$195$		0			0
$196$	37.9600	−	90.3495i	0.193673	−	0.460967i
$197$	−179.443			−0.910877			−0.455438	−	0.890267i	$-0.650517\pi$
$197$	−179.443			−0.910877			−0.455438	+	0.890267i	$0.650517\pi$
$198$	15.9888	+	27.6934i	0.0807516	+	0.139866i
$199$	−221.630	−	127.958i	−1.11372	−	0.643006i	−0.173928	−	0.984758i	$-0.555646\pi$
$199$	−221.630	−	127.958i	−1.11372	−	0.643006i	−0.939790	+	0.341753i	$0.888979\pi$
$200$		0			0
$201$	−99.8732	+	57.6618i	−0.496882	+	0.286875i
$202$			258.291i			1.27867i
$203$	4.38688	+	69.6257i	0.0216102	+	0.342984i
$204$	72.7026			0.356385
$205$		0			0
$206$	111.514	+	64.3825i	0.541329	+	0.312536i
$207$	−8.37014	+	14.4975i	−0.0404355	+	0.0700363i
$208$	−74.0994	+	42.7813i	−0.356247	+	0.205679i
$209$			181.661i			0.869190i
$210$		0			0
$211$	196.891			0.933132			0.466566	−	0.884486i	$-0.345491\pi$
$211$	196.891			0.933132			0.466566	+	0.884486i	$0.345491\pi$
$212$	49.7979	+	86.2525i	0.234896	+	0.406851i
$213$	102.157	+	58.9806i	0.479612	+	0.276904i
$214$	−36.4417	+	63.1189i	−0.170288	+	0.294948i
$215$		0			0
$216$		−	14.6969i		−	0.0680414i
$217$	20.4843	−	41.2749i	0.0943977	−	0.190207i
$218$	54.2512			0.248859
$219$	75.9128	+	131.485i	0.346634	+	0.600387i
$220$		0			0
$221$	224.467	−	388.789i	1.01569	−	1.75923i
$222$	−47.5103	+	27.4301i	−0.214010	+	0.123559i
$223$		−	431.015i		−	1.93280i	−0.257039	−	0.966401i	$-0.582747\pi$
$223$		−	431.015i		−	1.93280i	0.257039	−	0.966401i	$-0.417253\pi$
$224$	35.4700	+	17.6034i	0.158348	+	0.0785866i
$225$		0			0
$226$	140.401	+	243.182i	0.621245	+	1.07603i
$227$	151.637	+	87.5479i	0.668006	+	0.385673i	0.795321	−	0.606189i	$-0.207302\pi$
$227$	151.637	+	87.5479i	0.668006	+	0.385673i	−0.127315	+	0.991862i	$0.540636\pi$
$228$	41.7457	−	72.3057i	0.183095	−	0.317130i
$229$	29.0717	−	16.7846i	0.126951	−	0.0732951i	−0.435180	−	0.900344i	$-0.643315\pi$
$229$	29.0717	−	16.7846i	0.126951	−	0.0732951i	0.562131	+	0.827048i	$0.309982\pi$
$230$		0			0
$231$	−50.5779	−	76.1108i	−0.218952	−	0.329484i
$232$	−28.1888			−0.121504
$233$	77.4567	+	134.159i	0.332432	+	0.575790i	0.982988	−	0.183669i	$-0.0587973\pi$
$233$	77.4567	+	134.159i	0.332432	+	0.575790i	−0.650556	+	0.759458i	$0.725464\pi$
$234$	−78.5942	−	45.3764i	−0.335873	−	0.193916i
$235$		0			0
$236$	−145.872	+	84.2195i	−0.618104	+	0.356862i
$237$			171.033i			0.721658i
$238$	−207.354	+	13.0647i	−0.871235	+	0.0548935i
$239$	316.591			1.32465			0.662325	−	0.749217i	$-0.269570\pi$
$239$	316.591			1.32465			0.662325	+	0.749217i	$0.269570\pi$
$240$		0			0
$241$	202.219	+	116.751i	0.839084	+	0.484446i	0.856953	−	0.515395i	$-0.172355\pi$
$241$	202.219	+	116.751i	0.839084	+	0.484446i	−0.0178685	+	0.999840i	$0.505688\pi$
$242$	45.3896	−	78.6171i	0.187560	−	0.324864i
$243$	13.5000	−	7.79423i	0.0555556	−	0.0320750i
$244$		−	167.294i		−	0.685631i
$245$		0			0
$246$	125.126			0.508644
$247$	−257.777	−	446.484i	−1.04363	−	1.80763i
$248$	16.1241	+	9.30925i	0.0650165	+	0.0375373i
$249$	−23.3349	+	40.4172i	−0.0937143	+	0.162318i
$250$		0			0
$251$		−	56.6879i		−	0.225848i	−0.993604	−	0.112924i	$-0.963978\pi$
$251$		−	56.6879i		−	0.225848i	0.993604	−	0.112924i	$-0.0360217\pi$
$252$	2.64104	+	41.9169i	0.0104803	+	0.166337i
$253$	−42.0583			−0.166238
$254$	52.4060	+	90.7698i	0.206323	+	0.357361i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	251.528	−	145.219i	0.978706	−	0.565056i	0.0768270	−	0.997044i	$-0.475521\pi$
$257$	251.528	−	145.219i	0.978706	−	0.565056i	0.901879	+	0.431988i	$0.142188\pi$
$258$		−	85.1581i		−	0.330070i
$259$	130.574	−	86.7704i	0.504147	−	0.335021i
$260$		0			0
$261$	−14.9494	−	25.8931i	−0.0572773	−	0.0992072i
$262$	−24.5366	−	14.1662i	−0.0936510	−	0.0540694i
$263$	222.298	−	385.031i	0.845238	−	1.46399i	−0.0401768	−	0.999193i	$-0.512792\pi$
$263$	222.298	−	385.031i	0.845238	−	1.46399i	0.885415	−	0.464802i	$-0.153875\pi$
$264$	31.9776	−	18.4623i	0.121127	−	0.0699329i
$265$		0			0
$266$	−106.069	+	213.723i	−0.398755	+	0.803471i
$267$	−24.0906			−0.0902270
$268$	66.5822	+	115.324i	0.248441	+	0.430312i
$269$	−144.956	−	83.6902i	−0.538869	−	0.311116i	0.205752	−	0.978604i	$-0.434036\pi$
$269$	−144.956	−	83.6902i	−0.538869	−	0.311116i	−0.744620	+	0.667488i	$0.767369\pi$
$270$		0			0
$271$	2.24099	−	1.29384i	0.00826933	−	0.00477430i	−0.495860	−	0.868403i	$-0.665147\pi$
$271$	2.24099	−	1.29384i	0.00826933	−	0.00477430i	0.504129	+	0.863628i	$0.331814\pi$
$272$		−	83.9498i		−	0.308639i
$273$	232.311	+	115.294i	0.850957	+	0.422322i
$274$	−121.864			−0.444758
$275$		0			0
$276$	16.7403	+	9.66501i	0.0606532	+	0.0350181i
$277$	254.556	−	440.903i	0.918973	−	1.59171i	0.117996	−	0.993014i	$-0.462353\pi$
$277$	254.556	−	440.903i	0.918973	−	1.59171i	0.800978	−	0.598694i	$-0.204314\pi$
$278$	284.756	−	164.404i	1.02430	−	0.591381i
$279$			19.7479i			0.0707810i
$280$		0			0
$281$	210.688			0.749779			0.374890	−	0.927069i	$-0.377681\pi$
$281$	210.688			0.749779			0.374890	+	0.927069i	$0.377681\pi$
$282$	95.1005	+	164.719i	0.337236	+	0.584110i
$283$	34.1964	+	19.7433i	0.120835	+	0.0697643i	0.559199	−	0.829033i	$-0.311109\pi$
$283$	34.1964	+	19.7433i	0.120835	+	0.0697643i	−0.438364	+	0.898797i	$0.644442\pi$
$284$	68.1049	−	117.961i	0.239806	−	0.415356i
$285$		0			0
$286$		−	228.007i		−	0.797229i
$287$	−356.871	+	22.4852i	−1.24345	+	0.0783457i
$288$	−16.9706			−0.0589256
$289$	75.7363	+	131.179i	0.262063	+	0.453907i
$290$		0			0
$291$	−3.19678	+	5.53698i	−0.0109855	+	0.0190274i
$292$	151.826	−	87.6565i	0.519951	−	0.300194i
$293$		−	89.6023i		−	0.305810i	−0.988241	−	0.152905i	$-0.951137\pi$
$293$		−	89.6023i		−	0.305810i	0.988241	−	0.152905i	$-0.0488628\pi$
$294$	−15.0649	−	119.076i	−0.0512412	−	0.405020i
$295$		0			0
$296$	31.6735	+	54.8602i	0.107005	+	0.185338i
$297$	33.9174	+	19.5822i	0.114200	+	0.0659334i
$298$	155.511	−	269.354i	0.521850	−	0.903871i
$299$	103.370	−	59.6809i	0.345720	−	0.199602i
$300$		0			0
$301$	15.3029	+	242.878i	0.0508402	+	0.806903i
$302$	−368.999			−1.22185
$303$	158.170	+	273.959i	0.522013	+	0.904154i
$304$	−83.4914	−	48.2038i	−0.274643	−	0.158565i
$305$		0			0
$306$	77.1128	−	44.5211i	0.252003	−	0.145494i
$307$		−	470.478i		−	1.53250i	−0.642542	−	0.766251i	$-0.722120\pi$
$307$		−	470.478i		−	1.53250i	0.642542	−	0.766251i	$-0.277880\pi$
$308$	−87.8852	+	58.4024i	−0.285341	+	0.189618i
$309$	157.704			0.510370
$310$		0			0
$311$	217.631	+	125.649i	0.699778	+	0.404017i	0.807265	−	0.590189i	$-0.200947\pi$
$311$	217.631	+	125.649i	0.699778	+	0.404017i	−0.107487	+	0.994207i	$0.534280\pi$
$312$	−52.3962	+	90.7528i	−0.167936	+	0.290874i
$313$	−336.417	+	194.231i	−1.07482	+	0.620545i	−0.929493	−	0.368839i	$-0.879755\pi$
$313$	−336.417	+	194.231i	−1.07482	+	0.620545i	−0.145322	+	0.989384i	$0.546422\pi$
$314$			161.490i			0.514300i
$315$		0			0
$316$	197.492			0.624974
$317$	−74.6898	−	129.366i	−0.235614	−	0.408096i	0.723837	−	0.689971i	$-0.242377\pi$
$317$	−74.6898	−	129.366i	−0.235614	−	0.408096i	−0.959451	+	0.281875i	$0.909044\pi$
$318$	105.637	+	60.9897i	0.332193	+	0.191792i
$319$	37.5588	−	65.0538i	0.117739	−	0.203930i
$320$		0			0
$321$			89.2636i			0.278080i
$322$	−49.4815	−	24.5572i	−0.153669	−	0.0762645i
$323$	505.837			1.56606
$324$	−9.00000	−	15.5885i	−0.0277778	−	0.0481125i
$325$		0			0
$326$	−34.4475	+	59.6648i	−0.105667	+	0.183021i
$327$	57.5420	−	33.2219i	0.175970	−	0.101596i
$328$		−	144.484i		−	0.440499i
$329$	−300.835	−	452.702i	−0.914391	−	1.37600i
$330$		0			0
$331$	235.465	+	407.838i	0.711375	+	1.23214i	0.964341	+	0.264663i	$0.0852607\pi$
$331$	235.465	+	407.838i	0.711375	+	1.23214i	−0.252966	+	0.967475i	$0.581406\pi$
$332$	46.6697	+	26.9448i	0.140571	+	0.0811590i
$333$	−33.5948	+	58.1880i	−0.100885	+	0.174739i
$334$	60.7628	−	35.0814i	0.181925	−	0.105034i
$335$		0			0
$336$	48.4014	−	3.04961i	0.144052	−	0.00907622i
$337$	−532.478			−1.58005			−0.790027	−	0.613072i	$-0.789934\pi$
$337$	−532.478			−1.58005			−0.790027	+	0.613072i	$0.789934\pi$
$338$	204.042	+	353.412i	0.603676	+	1.04560i
$339$	297.836	+	171.956i	0.878573	+	0.507244i
$340$		0			0
$341$	−42.9675	+	24.8073i	−0.126004	+	0.0727487i
$342$		−	102.256i		−	0.298993i
$343$	64.3643	+	336.907i	0.187651	+	0.982236i
$344$	−98.3321			−0.285849
$345$		0			0
$346$	288.232	+	166.411i	0.833042	+	0.480957i
$347$	−224.812	+	389.385i	−0.647872	+	1.12215i	0.335758	+	0.941948i	$0.391008\pi$
$347$	−224.812	+	389.385i	−0.647872	+	1.12215i	−0.983630	+	0.180199i	$0.942326\pi$
$348$	−29.8988	+	17.2621i	−0.0859160	+	0.0496036i
$349$		−	330.676i		−	0.947495i	−0.880661	−	0.473747i	$-0.842901\pi$
$349$		−	330.676i		−	0.947495i	0.880661	−	0.473747i	$-0.157099\pi$
$350$		0			0
$351$	−111.149			−0.316664
$352$	−21.3184	−	36.9246i	−0.0605637	−	0.104899i
$353$	235.014	+	135.686i	0.665763	+	0.384379i	0.794469	−	0.607304i	$-0.207749\pi$
$353$	235.014	+	135.686i	0.665763	+	0.384379i	−0.128706	+	0.991683i	$0.541082\pi$
$354$	−103.147	+	178.657i	−0.291377	+	0.504680i
$355$		0			0
$356$			27.8174i			0.0781389i
$357$	−211.932	+	140.835i	−0.593646	+	0.394496i
$358$	−62.5221			−0.174643
$359$	3.79200	+	6.56794i	0.0105627	+	0.0182951i	0.871258	−	0.490825i	$-0.163304\pi$
$359$	3.79200	+	6.56794i	0.0105627	+	0.0182951i	−0.860696	+	0.509120i	$0.829971\pi$
$360$		0			0
$361$	109.950	−	190.440i	0.304572	−	0.527534i
$362$	143.355	−	82.7661i	0.396009	−	0.228636i
$363$		−	111.181i		−	0.306285i
$364$	133.130	−	268.250i	0.365741	−	0.736951i
$365$		0			0
$366$	−102.446	−	177.442i	−0.279908	−	0.484814i
$367$	460.216	+	265.706i	1.25400	+	0.723995i	0.971901	−	0.235392i	$-0.0756373\pi$
$367$	460.216	+	265.706i	1.25400	+	0.723995i	0.282095	+	0.959386i	$0.408971\pi$
$368$	11.1602	−	19.3300i	0.0303266	−	0.0525272i
$369$	132.717	−	76.6240i	0.359666	−	0.207653i
$370$		0			0
$371$	−312.246	−	154.965i	−0.841634	−	0.417695i
$372$	22.8029			0.0612981
$373$	−287.484	−	497.937i	−0.770734	−	1.33495i	−0.937161	−	0.348897i	$-0.886556\pi$
$373$	−287.484	−	497.937i	−0.770734	−	1.33495i	0.166427	−	0.986054i	$-0.446777\pi$
$374$	193.738	+	111.855i	0.518016	+	0.299077i
$375$		0			0
$376$	190.201	−	109.813i	0.505854	−	0.292055i
$377$			213.185i			0.565476i
$378$	28.4700	+	42.8423i	0.0753174	+	0.113339i
$379$	627.464			1.65558			0.827789	−	0.561040i	$-0.189598\pi$
$379$	627.464			1.65558			0.827789	+	0.561040i	$0.189598\pi$
$380$		0			0
$381$	111.170	+	64.1839i	0.291784	+	0.168462i
$382$	−165.684	+	286.973i	−0.433727	+	0.751238i
$383$	57.6870	−	33.3056i	0.150619	−	0.0869597i	−0.422797	−	0.906225i	$-0.638952\pi$
$383$	57.6870	−	33.3056i	0.150619	−	0.0869597i	0.573415	+	0.819265i	$0.305618\pi$
$384$			19.5959i			0.0510310i
$385$		0			0
$386$	−27.6691			−0.0716817
$387$	−52.1485	−	90.3238i	−0.134751	−	0.233395i
$388$	6.39356	+	3.69132i	0.0164782	+	0.00951372i
$389$	−274.525	+	475.491i	−0.705719	+	1.22234i	0.260713	+	0.965416i	$0.416043\pi$
$389$	−274.525	+	475.491i	−0.705719	+	1.22234i	−0.966431	+	0.256925i	$0.917291\pi$
$390$		0			0
$391$			117.112i			0.299519i
$392$	−137.497	+	17.3955i	−0.350757	+	0.0443762i
$393$	−34.7000			−0.0882950
$394$	126.885	+	219.772i	0.322044	+	0.557796i
$395$		0			0
$396$	22.6116	−	39.1644i	0.0571000	−	0.0989001i
$397$	−449.091	+	259.283i	−1.13121	+	0.653106i	−0.944240	−	0.329259i	$-0.893201\pi$
$397$	−449.091	+	259.283i	−1.13121	+	0.653106i	−0.186973	+	0.982365i	$0.559868\pi$
$398$			361.920i			0.909347i
$399$	18.3753	+	291.642i	0.0460535	+	0.730931i
$400$		0			0
$401$	238.149	+	412.486i	0.593888	+	1.02864i	0.993703	+	0.112048i	$0.0357411\pi$
$401$	238.149	+	412.486i	0.593888	+	1.02864i	−0.399815	+	0.916596i	$0.630926\pi$
$402$	141.242	+	81.5462i	0.351349	+	0.202851i
$403$	70.4033	−	121.942i	0.174698	−	0.302586i
$404$	316.340	−	182.639i	0.783020	−	0.452077i
$405$		0			0
$406$	82.1717	−	54.6056i	0.202393	−	0.134497i
$407$	−168.807			−0.414760
$408$	−51.4085	−	89.0422i	−0.126001	−	0.218241i
$409$	−93.2552	−	53.8409i	−0.228008	−	0.131640i	0.381645	−	0.924309i	$-0.375358\pi$
$409$	−93.2552	−	53.8409i	−0.228008	−	0.131640i	−0.609653	+	0.792669i	$0.708691\pi$
$410$		0			0
$411$	−129.256	+	74.6259i	−0.314491	+	0.181572i
$412$		−	182.101i		−	0.441993i
$413$	262.080	−	528.079i	0.634577	−	1.27864i
$414$	23.6743			0.0571844
$415$		0			0
$416$	104.792	+	60.5019i	0.251905	+	0.145437i
$417$	201.353	−	348.753i	0.482861	−	0.836339i
$418$	222.488	−	128.454i	0.532268	−	0.307305i
$419$			323.811i			0.772818i	0.922328	+	0.386409i	$0.126285\pi$
$419$			323.811i			0.772818i	−0.922328	+	0.386409i	$0.873715\pi$
$420$		0			0
$421$	−238.957			−0.567595			−0.283797	−	0.958884i	$-0.591594\pi$
$421$	−238.957			−0.567595			−0.283797	+	0.958884i	$0.591594\pi$
$422$	−139.223	−	241.141i	−0.329912	−	0.571424i
$423$	201.739	+	116.474i	0.476924	+	0.275352i
$424$	70.4249	−	121.979i	0.166096	−	0.287687i
$425$		0			0
$426$		−	166.822i		−	0.391601i
$427$	324.071	+	487.670i	0.758950	+	1.14208i
$428$	103.073			0.240824
$429$	−139.625	−	241.838i	−0.325467	−	0.563726i
$430$		0			0
$431$	95.8960	−	166.097i	0.222497	−	0.385375i	−0.733069	−	0.680154i	$-0.761913\pi$
$431$	95.8960	−	166.097i	0.222497	−	0.385375i	0.955565	+	0.294779i	$0.0952461\pi$
$432$	−18.0000	+	10.3923i	−0.0416667	+	0.0240563i
$433$		−	122.083i		−	0.281946i	−0.990013	−	0.140973i	$-0.954977\pi$
$433$		−	122.083i		−	0.281946i	0.990013	−	0.140973i	$-0.0450231\pi$
$434$	−65.0358	+	4.09768i	−0.149852	+	0.00944166i
$435$		0			0
$436$	−38.3614	−	66.4438i	−0.0879848	−	0.152394i
$437$	116.472	+	67.2454i	0.266527	+	0.153880i
$438$	107.357	−	185.948i	0.245107	−	0.424538i
$439$	−217.656	+	125.664i	−0.495800	+	0.286250i	−0.726978	−	0.686661i	$-0.759076\pi$
$439$	−217.656	+	125.664i	−0.495800	+	0.286250i	0.231177	+	0.972912i	$0.425742\pi$
$440$		0			0
$441$	−88.8975	−	117.074i	−0.201582	−	0.265473i
$442$	−634.890			−1.43640
$443$	54.8946	+	95.0802i	0.123916	+	0.214628i	0.921309	−	0.388832i	$-0.127121\pi$
$443$	54.8946	+	95.0802i	0.123916	+	0.214628i	−0.797393	+	0.603460i	$0.793788\pi$
$444$	67.1897	+	38.7920i	0.151328	+	0.0873693i
$445$		0			0
$446$	−527.883	+	304.773i	−1.18359	+	0.683349i
$447$		−	380.924i		−	0.852178i
$448$	−3.52139	−	55.8892i	−0.00786024	−	0.124753i
$449$	806.490			1.79619			0.898095	−	0.439801i	$-0.144951\pi$
$449$	806.490			1.79619			0.898095	+	0.439801i	$0.144951\pi$
$450$		0			0
$451$	333.437	+	192.510i	0.739329	+	0.426852i
$452$	198.558	−	343.912i	0.439287	−	0.760867i
$453$	−391.383	+	225.965i	−0.863980	+	0.498819i
$454$		−	247.623i		−	0.545425i
$455$		0			0
$456$	−118.075			−0.258936
$457$	−386.226	−	668.964i	−0.845135	−	1.46382i	−0.885504	−	0.464631i	$-0.846187\pi$
$457$	−386.226	−	668.964i	−0.845135	−	1.46382i	0.0403698	−	0.999185i	$-0.487146\pi$
$458$	−41.1137	−	23.7370i	−0.0897678	−	0.0518275i
$459$	54.5270	−	94.4435i	0.118795	−	0.205759i
$460$		0			0
$461$		−	793.611i		−	1.72150i	−0.509029	−	0.860749i	$-0.669995\pi$
$461$		−	793.611i		−	1.72150i	0.509029	−	0.860749i	$-0.330005\pi$
$462$	−57.4523	+	115.764i	−0.124356	+	0.250570i
$463$	274.227			0.592284			0.296142	−	0.955144i	$-0.404300\pi$
$463$	274.227			0.592284			0.296142	+	0.955144i	$0.404300\pi$
$464$	19.9325	+	34.5241i	0.0429580	+	0.0744054i
$465$		0			0
$466$	109.540	−	189.730i	0.235065	−	0.407145i
$467$	−344.357	+	198.815i	−0.737381	+	0.425727i	−0.821116	−	0.570761i	$-0.806648\pi$
$467$	−344.357	+	198.815i	−0.737381	+	0.425727i	0.0837354	+	0.996488i	$0.473315\pi$
$468$			128.344i			0.274239i
$469$	−417.488	−	207.195i	−0.890166	−	0.441781i
$470$		0			0
$471$	98.8921	+	171.286i	0.209962	+	0.363665i
$472$	206.295	+	119.104i	0.437065	+	0.252340i
$473$	131.018	−	226.930i	0.276993	−	0.479766i
$474$	209.472	−	120.939i	0.441923	−	0.255145i
$475$		0			0
$476$	162.622	+	244.717i	0.341643	+	0.514112i
$477$	149.394			0.313194
$478$	−223.864	−	387.743i	−0.468334	−	0.811179i
$479$	−165.573	−	95.5938i	−0.345665	−	0.199570i	0.317110	−	0.948389i	$-0.397288\pi$
$479$	−165.573	−	95.5938i	−0.345665	−	0.199570i	−0.662774	+	0.748819i	$0.730621\pi$
$480$		0			0
$481$	414.893	−	239.538i	0.862563	−	0.498001i
$482$		−	330.223i		−	0.685110i
$483$	−67.5212	+	4.25428i	−0.139795	+	0.00880803i
$484$	−128.381			−0.265250
$485$		0			0
$486$	−19.0919	−	11.0227i	−0.0392837	−	0.0226805i
$487$	−95.0092	+	164.561i	−0.195091	+	0.337907i	−0.946930	−	0.321439i	$-0.895833\pi$
$487$	−95.0092	+	164.561i	−0.195091	+	0.337907i	0.751840	+	0.659346i	$0.229167\pi$
$488$	−204.892	+	118.295i	−0.419862	+	0.242407i
$489$			84.3788i			0.172554i
$490$		0			0
$491$	−211.384			−0.430517			−0.215258	−	0.976557i	$-0.569059\pi$
$491$	−211.384			−0.430517			−0.215258	+	0.976557i	$0.569059\pi$
$492$	−88.4777	−	153.248i	−0.179833	−	0.311480i
$493$	−181.143	−	104.583i	−0.367430	−	0.212136i
$494$	−364.552	+	631.423i	−0.737960	+	1.27818i
$495$		0			0
$496$		−	26.3305i		−	0.0530857i
$497$	29.9779	+	475.791i	0.0603178	+	0.957325i
$498$	66.0010			0.132532
$499$	126.864	+	219.734i	0.254236	+	0.440349i	0.964688	−	0.263396i	$-0.0848427\pi$
$499$	126.864	+	219.734i	0.254236	+	0.440349i	−0.710452	+	0.703746i	$0.751509\pi$
$500$		0			0
$501$	42.9658	−	74.4190i	0.0857601	−	0.148541i
$502$	−69.4282	+	40.0844i	−0.138303	+	0.0798494i
$503$			217.815i			0.433033i	0.976279	+	0.216516i	$0.0694695\pi$
$503$			217.815i			0.433033i	−0.976279	+	0.216516i	$0.930531\pi$
$504$	49.4700	−	32.8743i	0.0981547	−	0.0652268i
$505$		0			0
$506$	29.7397	+	51.5107i	0.0587741	+	0.101800i
$507$	432.839	+	249.900i	0.853727	+	0.492899i
$508$	74.1132	−	128.368i	0.145892	−	0.252693i
$509$	−24.6582	+	14.2364i	−0.0484444	+	0.0279694i	−0.524027	−	0.851702i	$-0.675571\pi$
$509$	−24.6582	+	14.2364i	−0.0484444	+	0.0279694i	0.475582	+	0.879671i	$0.342237\pi$
$510$		0			0
$511$	−272.776	+	549.630i	−0.533808	+	1.07560i
$512$	22.6274			0.0441942
$513$	−62.6185	−	108.458i	−0.122063	−	0.211420i
$514$	−355.714	−	205.371i	−0.692050	−	0.399555i
$515$		0			0
$516$	−104.297	+	60.2159i	−0.202126	+	0.116697i
$517$			585.258i			1.13203i
$518$	−198.601	−	98.5640i	−0.383400	−	0.190278i
$519$	407.622			0.785399
$520$		0			0
$521$	671.401	+	387.634i	1.28868	+	0.744019i	0.978418	−	0.206633i	$-0.0662507\pi$
$521$	671.401	+	387.634i	1.28868	+	0.744019i	0.310260	+	0.950652i	$0.399584\pi$
$522$	−21.1416	+	36.6184i	−0.0405012	+	0.0701501i
$523$	88.7388	−	51.2334i	0.169673	−	0.0979605i	−0.412759	−	0.910840i	$-0.635435\pi$
$523$	88.7388	−	51.2334i	0.169673	−	0.0979605i	0.582431	+	0.812880i	$0.302101\pi$
$524$			40.0681i			0.0764657i
$525$		0			0
$526$	−628.752			−1.19535
$527$	69.0763	+	119.644i	0.131075	+	0.227028i
$528$	−45.2232	−	26.1096i	−0.0856500	−	0.0494501i
$529$	248.931	−	431.162i	0.470570	−	0.815050i
$530$		0			0
$531$			252.659i			0.475816i
$532$	336.759	−	21.2180i	0.633005	−	0.0398835i
$533$	−1092.69			−2.05008
$534$	17.0346	+	29.5049i	0.0319001	+	0.0552525i
$535$		0			0
$536$	94.1614	−	163.092i	0.175674	−	0.304277i
$537$	−66.3147	+	38.2868i	−0.123491	+	0.0712976i
$538$			236.712i			0.439984i
$539$	143.056	−	340.491i	0.265410	−	0.631709i
$540$		0			0
$541$	408.868	+	708.180i	0.755763	+	1.30902i	0.944994	+	0.327088i	$0.106067\pi$
$541$	408.868	+	708.180i	0.755763	+	1.30902i	−0.189231	+	0.981933i	$0.560599\pi$
$542$	−3.16924	−	1.82976i	−0.00584730	−	0.00337594i
$543$	101.367	−	175.573i	0.186680	−	0.323340i
$544$	−102.817	+	59.3614i	−0.189002	+	0.109120i
$545$		0			0
$546$	−23.0634	−	366.047i	−0.0422406	−	0.670416i
$547$	204.209			0.373325			0.186662	−	0.982424i	$-0.440233\pi$
$547$	204.209			0.373325			0.186662	+	0.982424i	$0.440233\pi$
$548$	86.1706	+	149.252i	0.157246	+	0.272357i
$549$	−217.321	−	125.471i	−0.395849	−	0.228544i
$550$		0			0
$551$	−208.024	+	120.103i	−0.377539	+	0.217972i
$552$		−	27.3368i		−	0.0495231i
$553$	−575.698	+	382.569i	−1.04105	+	0.691806i
$554$	−719.992			−1.29962
$555$		0			0
$556$	−402.706	−	232.502i	−0.724291	−	0.418169i
$557$	268.036	−	464.253i	0.481214	−	0.833487i	−0.518553	−	0.855045i	$-0.673529\pi$
$557$	268.036	−	464.253i	0.481214	−	0.833487i	0.999768	+	0.0215578i	$0.00686259\pi$
$558$	24.1861	−	13.9639i	0.0433443	−	0.0250249i
$559$			743.660i			1.33034i
$560$		0			0
$561$	273.987			0.488391
$562$	−148.979	−	258.039i	−0.265087	−	0.459144i
$563$	857.029	+	494.806i	1.52225	+	0.878874i	0.999654	+	0.0262960i	$0.00837123\pi$
$563$	857.029	+	494.806i	1.52225	+	0.878874i	0.522600	+	0.852578i	$0.324962\pi$
$564$	134.492	−	232.948i	0.238462	−	0.413028i
$565$		0			0
$566$		−	55.8424i		−	0.0986616i
$567$	56.4324	+	28.0068i	0.0995281	+	0.0493948i
$568$	−192.630			−0.339137
$569$	−248.330	−	430.120i	−0.436432	−	0.755922i	0.560979	−	0.827830i	$-0.310425\pi$
$569$	−248.330	−	430.120i	−0.436432	−	0.755922i	−0.997411	+	0.0719076i	$0.977091\pi$
$570$		0			0
$571$	71.0244	−	123.018i	0.124386	−	0.215443i	−0.797107	−	0.603838i	$-0.793637\pi$
$571$	71.0244	−	123.018i	0.124386	−	0.215443i	0.921493	+	0.388395i	$0.126971\pi$
$572$	−279.251	+	161.226i	−0.488201	+	0.281863i
$573$			405.841i			0.708274i
$574$	279.884	+	421.176i	0.487604	+	0.733757i
$575$		0			0
$576$	12.0000	+	20.7846i	0.0208333	+	0.0360844i
$577$	328.551	+	189.689i	0.569413	+	0.328751i	0.756915	−	0.653514i	$-0.226706\pi$
$577$	328.551	+	189.689i	0.569413	+	0.328751i	−0.187502	+	0.982264i	$0.560039\pi$
$578$	107.107	−	185.515i	0.185307	−	0.320961i
$579$	−29.3476	+	16.9438i	−0.0506866	+	0.0292639i
$580$		0			0
$581$	−188.240	+	11.8604i	−0.323993	+	0.0204137i
$582$	9.04185			0.0155358
$583$	187.668	+	325.051i	0.321901	+	0.557549i
$584$	−214.714	−	123.965i	−0.367661	−	0.212269i
$585$		0			0
$586$	−109.740	+	63.3584i	−0.187269	+	0.108120i
$587$			234.204i			0.398984i	0.979899	+	0.199492i	$0.0639292\pi$
$587$			234.204i			0.398984i	−0.979899	+	0.199492i	$0.936071\pi$
$588$	−135.185	+	102.650i	−0.229906	+	0.174575i
$589$	158.654			0.269361
$590$		0			0
$591$	269.164	+	155.402i	0.455438	+	0.262948i
$592$	44.7931	−	77.5840i	0.0756641	−	0.131054i
$593$	495.838	−	286.272i	0.836152	−	0.482753i	−0.0198023	−	0.999804i	$-0.506304\pi$
$593$	495.838	−	286.272i	0.836152	−	0.482753i	0.855954	+	0.517051i	$0.172970\pi$
$594$		−	55.3869i		−	0.0932439i
$595$		0			0
$596$	−439.853			−0.738008
$597$	221.630	+	383.874i	0.371239	+	0.643006i
$598$	−146.188	−	84.4016i	−0.244461	−	0.141140i
$599$	−46.7105	+	80.9049i	−0.0779807	+	0.135067i	−0.902379	−	0.430944i	$-0.858181\pi$
$599$	−46.7105	+	80.9049i	−0.0779807	+	0.135067i	0.824398	+	0.566011i	$0.191514\pi$
$600$		0			0
$601$			167.140i			0.278103i	0.990285	+	0.139051i	$0.0444053\pi$
$601$			167.140i			0.278103i	−0.990285	+	0.139051i	$0.955595\pi$
$602$	286.643	−	190.483i	0.476151	−	0.316417i
$603$	199.746			0.331255
$604$	260.922	+	451.930i	0.431990	+	0.748229i
$605$		0			0
$606$	223.686	−	387.436i	0.369119	−	0.639333i
$607$	796.002	−	459.572i	1.31137	−	0.757120i	0.329047	−	0.944314i	$-0.393273\pi$
$607$	796.002	−	459.572i	1.31137	−	0.757120i	0.982323	+	0.187194i	$0.0599392\pi$
$608$			136.341i			0.224245i
$609$	53.7173	−	108.238i	0.0882058	−	0.177730i
$610$		0			0
$611$	−830.484	−	1438.44i	−1.35922	−	2.35424i
$612$	−109.054	−	62.9623i	−0.178193	−	0.102880i
$613$	−389.718	+	675.011i	−0.635755	+	1.10116i	0.350600	+	0.936525i	$0.385978\pi$
$613$	−389.718	+	675.011i	−0.635755	+	1.10116i	−0.986355	+	0.164635i	$0.947356\pi$
$614$	−576.215	+	332.678i	−0.938462	+	0.541821i
$615$		0			0
$616$	133.672	+	66.3402i	0.217000	+	0.107695i
$617$	−510.821			−0.827911			−0.413956	−	0.910297i	$-0.635853\pi$
$617$	−510.821			−0.827911			−0.413956	+	0.910297i	$0.635853\pi$
$618$	−111.514	−	193.148i	−0.180443	−	0.312536i
$619$	−808.792	−	466.956i	−1.30661	−	0.754372i	−0.325082	−	0.945686i	$-0.605392\pi$
$619$	−808.792	−	466.956i	−1.30661	−	0.754372i	−0.981529	+	0.191314i	$0.938725\pi$
$620$		0			0
$621$	25.1104	−	14.4975i	0.0404355	−	0.0233454i
$622$		−	355.390i		−	0.571367i
$623$	−53.8862	−	81.0892i	−0.0864947	−	0.130159i
$624$	148.199			0.237498
$625$		0			0
$626$	475.766	+	274.684i	0.760009	+	0.438792i
$627$	157.323	−	272.491i	0.250914	−	0.434595i
$628$	197.784	−	114.191i	0.314943	−	0.181832i
$629$			470.047i			0.747292i
$630$		0			0
$631$	−614.861			−0.974423			−0.487212	−	0.873284i	$-0.661986\pi$
$631$	−614.861			−0.974423			−0.487212	+	0.873284i	$0.661986\pi$
$632$	−139.648	−	241.877i	−0.220962	−	0.382717i
$633$	−295.336	−	170.512i	−0.466566	−	0.269372i
$634$	−105.627	+	182.952i	−0.166605	+	0.288568i
$635$		0			0
$636$		−	172.505i		−	0.271234i
$637$	131.557	+	1039.85i	0.206526	+	1.63242i
$638$	−106.232			−0.166508
$639$	−102.157	−	176.942i	−0.159871	−	0.276904i
$640$		0			0
$641$	94.1724	−	163.111i	0.146915	−	0.254464i	−0.783171	−	0.621807i	$-0.786399\pi$
$641$	94.1724	−	163.111i	0.146915	−	0.254464i	0.930086	+	0.367343i	$0.119732\pi$
$642$	109.325	−	63.1189i	0.170288	−	0.0983161i
$643$		−	23.8831i		−	0.0371432i	−0.999828	−	0.0185716i	$-0.994088\pi$
$643$		−	23.8831i		−	0.0371432i	0.999828	−	0.0185716i	$-0.00591187\pi$
$644$	4.91242	+	77.9667i	0.00762798	+	0.121066i
$645$		0			0
$646$	−357.681	−	619.521i	−0.553685	−	0.959011i
$647$	939.928	+	542.667i	1.45275	+	0.838744i	0.998637	−	0.0522010i	$-0.0166237\pi$
$647$	939.928	+	542.667i	1.45275	+	0.838744i	0.454111	+	0.890945i	$0.349957\pi$
$648$	−12.7279	+	22.0454i	−0.0196419	+	0.0340207i
$649$	−549.735	+	317.390i	−0.847049	+	0.489044i
$650$		0			0
$651$	−66.4715	+	44.1724i	−0.102107	+	0.0678531i
$652$	97.4323			0.149436
$653$	−317.852	−	550.536i	−0.486756	−	0.843087i	0.513128	−	0.858312i	$-0.328487\pi$
$653$	−317.852	−	550.536i	−0.486756	−	0.843087i	−0.999884	+	0.0152254i	$0.995153\pi$
$654$	−81.3767	−	46.9829i	−0.124429	−	0.0718393i
$655$		0			0
$656$	−176.955	+	102.165i	−0.269749	+	0.155740i
$657$		−	262.970i		−	0.400258i
$658$	−341.723	+	688.555i	−0.519336	+	1.04644i
$659$	−888.955			−1.34895			−0.674473	−	0.738300i	$-0.735629\pi$
$659$	−888.955			−1.34895			−0.674473	+	0.738300i	$0.735629\pi$
$660$		0			0
$661$	−656.362	−	378.951i	−0.992983	−	0.573299i	−0.0868187	−	0.996224i	$-0.527670\pi$
$661$	−656.362	−	378.951i	−0.992983	−	0.573299i	−0.906165	+	0.422925i	$0.861003\pi$
$662$	332.998	−	576.770i	0.503018	−	0.871253i
$663$	−673.402	+	388.789i	−1.01569	+	0.586409i
$664$		−	76.2114i		−	0.114776i
$665$		0			0
$666$	95.0206			0.142674
$667$	−27.8063	−	48.1620i	−0.0416886	−	0.0722068i
$668$	−85.9316	−	49.6127i	−0.128640	−	0.0742704i
$669$	−373.270	+	646.522i	−0.557952	+	0.966401i
$670$		0			0
$671$		−	630.464i		−	0.939589i
$672$	−37.9600	−	57.1230i	−0.0564881	−	0.0850045i
$673$	−936.839			−1.39203			−0.696017	−	0.718026i	$-0.745046\pi$
$673$	−936.839			−1.39203			−0.696017	+	0.718026i	$0.745046\pi$
$674$	376.519	+	652.150i	0.558634	+	0.967582i
$675$		0			0
$676$	288.560	−	499.800i	0.426863	−	0.739349i
$677$	−214.062	+	123.589i	−0.316192	+	0.182554i	−0.649694	−	0.760196i	$-0.725103\pi$
$677$	−214.062	+	123.589i	−0.316192	+	0.182554i	0.333502	+	0.942749i	$0.391770\pi$
$678$		−	486.365i		−	0.717352i
$679$	−25.7881	+	1.62482i	−0.0379795	+	0.00239296i
$680$		0			0
$681$	−151.637	−	262.644i	−0.222669	−	0.385673i
$682$	60.7652	+	35.0828i	0.0890986	+	0.0514411i
$683$	−350.887	+	607.755i	−0.513744	+	0.889831i	0.486129	+	0.873887i	$0.338409\pi$
$683$	−350.887	+	607.755i	−0.513744	+	0.889831i	−0.999873	+	0.0159438i	$0.994925\pi$
$684$	−125.237	+	72.3057i	−0.183095	+	0.105710i
$685$		0			0
$686$	367.112	−	317.059i	0.535149	−	0.462185i
$687$	−58.1435			−0.0846339
$688$	69.5313	+	120.432i	0.101063	+	0.175046i
$689$	−922.498	−	532.604i	−1.33889	−	0.773011i
$690$		0			0
$691$	−530.850	+	306.486i	−0.768234	+	0.443540i	−0.832244	−	0.554409i	$-0.812944\pi$
$691$	−530.850	+	306.486i	−0.768234	+	0.443540i	0.0640104	+	0.997949i	$0.479611\pi$
$692$		−	470.682i		−	0.680176i
$693$	9.95302	+	157.968i	0.0143622	+	0.227948i
$694$	635.863			0.916230
$695$		0			0
$696$	42.2832	+	24.4122i	0.0607518	+	0.0350750i
$697$	536.047	−	928.461i	0.769078	−	1.33208i
$698$	−404.993	+	233.823i	−0.580220	+	0.334990i
$699$		−	268.318i		−	0.383860i
$700$		0			0
$701$	161.307			0.230110			0.115055	−	0.993359i	$-0.463296\pi$
$701$	161.307			0.230110			0.115055	+	0.993359i	$0.463296\pi$
$702$	78.5942	+	136.129i	0.111958	+	0.193916i
$703$	467.480	+	269.900i	0.664979	+	0.383926i
$704$	−30.1488	+	52.2193i	−0.0428250	+	0.0741751i
$705$		0			0
$706$		−	383.777i		−	0.543593i
$707$	−568.349	+	1145.20i	−0.803889	+	1.61980i
$708$	291.745			0.412069
$709$	−285.175	−	493.938i	−0.402222	−	0.696669i	0.591772	−	0.806106i	$-0.298429\pi$
$709$	−285.175	−	493.938i	−0.402222	−	0.696669i	−0.993994	+	0.109436i	$0.965095\pi$
$710$		0			0
$711$	148.119	−	256.549i	0.208325	−	0.360829i
$712$	34.0693	−	19.6699i	0.0478501	−	0.0276263i
$713$			36.7317i			0.0515171i
$714$	322.345	+	159.977i	0.451464	+	0.224057i
$715$		0			0
$716$	44.2098	+	76.5736i	0.0617455	+	0.106946i
$717$	−474.887	−	274.176i	−0.662325	−	0.382393i
$718$	5.36270	−	9.28847i	0.00746894	−	0.0129366i
$719$	431.817	−	249.310i	0.600580	−	0.346745i	−0.168690	−	0.985669i	$-0.553954\pi$
$719$	431.817	−	249.310i	0.600580	−	0.346745i	0.769270	+	0.638924i	$0.220620\pi$
$720$		0			0
$721$	352.755	+	530.834i	0.489258	+	0.736246i
$722$	−310.987			−0.430730
$723$	−202.219	−	350.254i	−0.279695	−	0.484446i
$724$	−202.735	−	117.049i	−0.280020	−	0.161670i
$725$		0			0
$726$	−136.169	+	78.6171i	−0.187560	+	0.108288i
$727$			1058.79i			1.45638i	0.685375	+	0.728190i	$0.259638\pi$
$727$			1058.79i			1.45638i	−0.685375	+	0.728190i	$0.740362\pi$
$728$	−422.675	+	26.6313i	−0.580597	+	0.0365815i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	−631.888	−	364.821i	−0.864416	−	0.499071i
$732$	−144.881	+	250.941i	−0.197925	+	0.342816i
$733$	−13.1068	+	7.56721i	−0.0178810	+	0.0103236i	−0.508914	−	0.860817i	$-0.669953\pi$
$733$	−13.1068	+	7.56721i	−0.0178810	+	0.0103236i	0.491033	+	0.871141i	$0.336620\pi$
$734$		−	751.530i		−	1.02388i
$735$		0			0
$736$	−31.5658			−0.0428883
$737$	250.922	+	434.609i	0.340463	+	0.589700i
$738$	−187.690	−	108.363i	−0.254322	−	0.146833i
$739$	81.3819	−	140.958i	0.110124	−	0.190741i	−0.805696	−	0.592329i	$-0.798208\pi$
$739$	81.3819	−	140.958i	0.110124	−	0.190741i	0.915820	+	0.401588i	$0.131542\pi$
$740$		0			0
$741$			892.967i			1.20508i
$742$	30.9991	+	491.998i	0.0417778	+	0.663071i
$743$	−338.071			−0.455009			−0.227504	−	0.973777i	$-0.573057\pi$
$743$	−338.071			−0.455009			−0.227504	+	0.973777i	$0.573057\pi$
$744$	−16.1241	−	27.9277i	−0.0216722	−	0.0375373i
$745$		0			0
$746$	−406.564	+	704.189i	−0.544991	+	0.943953i
$747$	70.0046	−	40.4172i	0.0937143	−	0.0541060i
$748$		−	316.373i		−	0.422959i
$749$	−300.462	+	199.666i	−0.401151	+	0.266577i
$750$		0			0
$751$	−239.087	−	414.111i	−0.318359	−	0.551413i	0.661787	−	0.749692i	$-0.269798\pi$
$751$	−239.087	−	414.111i	−0.318359	−	0.551413i	−0.980146	+	0.198279i	$0.936465\pi$
$752$	−268.985	−	155.299i	−0.357693	−	0.206514i
$753$	−49.0932	+	85.0319i	−0.0651968	+	0.112924i
$754$	261.097	−	150.744i	0.346282	−	0.199926i
$755$		0			0
$756$	32.3395	−	65.1625i	0.0427771	−	0.0861938i
$757$	397.788			0.525479			0.262739	−	0.964867i	$-0.415374\pi$
$757$	397.788			0.525479			0.262739	+	0.964867i	$0.415374\pi$
$758$	−443.684	−	768.483i	−0.585335	−	1.01383i
$759$	63.0874	+	36.4236i	0.0831192	+	0.0479889i
$760$		0			0
$761$	−1264.02	+	729.785i	−1.66100	+	0.958981i	−0.688767	+	0.724983i	$0.741848\pi$
$761$	−1264.02	+	729.785i	−1.66100	+	0.958981i	−0.972237	+	0.233998i	$0.924819\pi$
$762$		−	181.540i		−	0.238241i
$763$	240.536	+	119.376i	0.315250	+	0.156456i
$764$	468.625			0.613383
$765$		0			0
$766$	−81.5817	−	47.1012i	−0.106503	−	0.0614898i
$767$	900.755	−	1560.15i	1.17439	−	2.03410i
$768$	24.0000	−	13.8564i	0.0312500	−	0.0180422i
$769$		−	2.10093i		−	0.00273203i	−0.999999	−	0.00136602i	$-0.999565\pi$
$769$		−	2.10093i		−	0.00273203i	0.999999	−	0.00136602i	$-0.000434817\pi$
$770$		0			0
$771$	−503.055			−0.652471
$772$	19.5650	+	33.8876i	0.0253433	+	0.0438959i
$773$	−391.972	−	226.305i	−0.507079	−	0.292762i	0.224553	−	0.974462i	$-0.427908\pi$
$773$	−391.972	−	226.305i	−0.507079	−	0.292762i	−0.731632	+	0.681700i	$0.761241\pi$
$774$	−73.7491	+	127.737i	−0.0952830	+	0.165035i
$775$		0			0
$776$		−	10.4406i		−	0.0134544i
$777$	−271.007	+	17.0752i	−0.348786	+	0.0219758i
$778$	776.473			0.998037
$779$	−615.594	−	1066.24i	−0.790236	−	1.36873i
$780$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +2.44949i q^{6} +(-0.440173 - 6.98615i) q^{7} +2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +2.44949i q^{6} +(-0.440173 - 6.98615i) q^{7} +2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(-3.76860 + 6.52741i) q^{11} +(3.00000 - 1.73205i) q^{12} -21.3906i q^{13} +(-8.24500 + 5.47905i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(18.1757 + 10.4937i) q^{17} +(2.12132 - 3.67423i) q^{18} +(20.8728 - 12.0509i) q^{19} +(-5.38992 + 10.8604i) q^{21} +10.6592 q^{22} +(2.79005 + 4.83250i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(-26.1981 + 15.1255i) q^{26} -5.19615i q^{27} +(12.5405 + 6.22374i) q^{28} -9.96625 q^{29} +(5.70073 + 3.29132i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(11.3058 - 6.52741i) q^{33} -29.6807i q^{34} -6.00000 q^{36} +(11.1983 + 19.3960i) q^{37} +(-29.5187 - 17.0426i) q^{38} +(-18.5248 + 32.0860i) q^{39} -51.0827i q^{41} +(17.1125 - 1.07820i) q^{42} -34.7656 q^{43} +(-7.53720 - 13.0548i) q^{44} +(3.94572 - 6.83419i) q^{46} +(67.2462 - 38.8246i) q^{47} +6.92820i q^{48} +(-48.6125 + 6.15023i) q^{49} +(-18.1757 - 31.4812i) q^{51} +(37.0497 + 21.3906i) q^{52} +(24.8989 - 43.1262i) q^{53} +(-6.36396 + 3.67423i) q^{54} +(-1.24500 - 19.7598i) q^{56} -41.7457 q^{57} +(7.04720 + 12.2061i) q^{58} +(72.9362 + 42.1098i) q^{59} +(-72.4404 + 41.8235i) q^{61} -9.30925i q^{62} +(17.4903 - 11.6228i) q^{63} +8.00000 q^{64} +(-15.9888 - 9.23115i) q^{66} +(33.2911 - 57.6618i) q^{67} +(-36.3513 + 20.9874i) q^{68} -9.66501i q^{69} -68.1049 q^{71} +(4.24264 + 7.34847i) q^{72} +(-75.9128 - 43.8283i) q^{73} +(15.8368 - 27.4301i) q^{74} +48.2038i q^{76} +(47.2603 + 23.4548i) q^{77} +52.3962 q^{78} +(-49.3730 - 85.5165i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-62.5632 + 36.1209i) q^{82} -26.9448i q^{83} +(-13.4209 - 20.1960i) q^{84} +(24.5830 + 42.5790i) q^{86} +(14.9494 + 8.63103i) q^{87} +(-10.6592 + 18.4623i) q^{88} +(12.0453 - 6.95436i) q^{89} +(-149.438 + 9.41559i) q^{91} -11.1602 q^{92} +(-5.70073 - 9.87395i) q^{93} +(-95.1005 - 54.9063i) q^{94} +(8.48528 - 4.89898i) q^{96} -3.69132i q^{97} +(41.9067 + 55.1890i) q^{98} -22.6116 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{3} - 8 q^{4} + 12 q^{9}+O(q^{10}) \) 8 * q - 12 * q^3 - 8 * q^4 + 12 * q^9	\( 8 q - 12 q^{3} - 8 q^{4} + 12 q^{9} - 4 q^{11} + 24 q^{12} - 16 q^{14} - 16 q^{16} - 24 q^{17} + 72 q^{19} + 24 q^{22} + 60 q^{23} - 72 q^{26} - 24 q^{29} + 96 q^{31} + 12 q^{33} - 48 q^{36} - 24 q^{37} - 180 q^{38} - 12 q^{39} + 12 q^{42} - 112 q^{43} - 8 q^{44} + 32 q^{46} + 84 q^{47} - 264 q^{49} + 24 q^{51} + 24 q^{52} + 44 q^{53} + 40 q^{56} - 144 q^{57} + 104 q^{58} + 312 q^{59} - 204 q^{61} + 64 q^{64} - 36 q^{66} + 120 q^{67} + 48 q^{68} - 64 q^{71} + 84 q^{73} - 16 q^{74} + 228 q^{77} + 144 q^{78} - 144 q^{79} - 36 q^{81} - 60 q^{82} + 176 q^{86} + 36 q^{87} - 24 q^{88} - 336 q^{89} - 296 q^{91} - 240 q^{92} - 96 q^{93} + 36 q^{94} - 24 q^{99}+O(q^{100}) \) 8 * q - 12 * q^3 - 8 * q^4 + 12 * q^9 - 4 * q^11 + 24 * q^12 - 16 * q^14 - 16 * q^16 - 24 * q^17 + 72 * q^19 + 24 * q^22 + 60 * q^23 - 72 * q^26 - 24 * q^29 + 96 * q^31 + 12 * q^33 - 48 * q^36 - 24 * q^37 - 180 * q^38 - 12 * q^39 + 12 * q^42 - 112 * q^43 - 8 * q^44 + 32 * q^46 + 84 * q^47 - 264 * q^49 + 24 * q^51 + 24 * q^52 + 44 * q^53 + 40 * q^56 - 144 * q^57 + 104 * q^58 + 312 * q^59 - 204 * q^61 + 64 * q^64 - 36 * q^66 + 120 * q^67 + 48 * q^68 - 64 * q^71 + 84 * q^73 - 16 * q^74 + 228 * q^77 + 144 * q^78 - 144 * q^79 - 36 * q^81 - 60 * q^82 + 176 * q^86 + 36 * q^87 - 24 * q^88 - 336 * q^89 - 296 * q^91 - 240 * q^92 - 96 * q^93 + 36 * q^94 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more